Stochastic, fuzzy, and game theoretical methods for the automatic design of Supply Chain Networks

We present the results of our research, developed during the recent years, regarding the implementation of innovative and automatic decision approaches for the design of modern Supply Chain Networks (SCNs). More in detail, we first present two alternative methods for the resolution of the so-called Supplier Selection Problem (SSP), one of the most difficult and emerging problems in SCN Design (SCND), where outsourcing is simultaneously becoming the key to success and the way to disruption. We present two novel methods for solving the SSP under uncertainty at a single level of the SCN, respectively based on the stochastic and the fuzzy cross-efficiency Data Envelopment Analysis (DEA) techniques. These methods allow ranking the candidate stakeholders on the basis of their efficiency values under uncertain parameters when either statistical or subjective information characterizes suppliers’ data. Then, we show in a third contribution the extension of the fuzzy cross-efficiency DEA technique to the order allocation problem (another significant and difficult task for the SCN decision maker) in a single-buyer multi-sellers environment. In particular, we join the previous method with a fuzzy linear programming model that fulfills the estimated demand received from customers assigning quantities to the suppliers on the basis of a trade-off between the costs, the lead time, and the efficiency. Some suitable performance indicators are also proposed to compare possible alternative design solutions. A further extension regards the whole SCND, i.e., the multi-buyers multi-sellers environment, which leads to the development of a Decision Support System (DSS) for the SCND. The proposed DSS is based on the fuzzy approach and useful both for the decision maker of the centralized SCN and as a self-diagnosis tool for each stakeholder to investigate how to influence the buyers’ ordering behavior. Finally, we propose a further alternative that is a bargaining game model in its extensive form (i.e., with a time sequencing of moves) and in a fuzzy setting. This approach to SCND in a decentralized way allows modeling the real behavior of modern SCN stakeholders, which on the one hand act to maximize their own profit, on the other hand cooperate to maximize the overall efficiency of the SCN and minimize production costs and lead times. Assignments are determined taking into account stock levels, uncertain production or warehouse capacities, and customers’ demand. Overall, the proposed methods suitably support the SCN decision making process providing an agile, cooperative, and resource-efficient automatic design of multi-stage SCNs under uncertain parameters.